Select the correct S.I. unit for surface tension (force per unit length at a liquid interface).
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Akg/m^3
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Bkg/m^2
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Ckg/m
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DN/m
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EPa·s
Answer
Correct Answer: N/m
Explanation
Introduction / Context:Surface tension quantifies the tangential force acting along a line at a liquid interface. It strongly affects capillarity, droplet formation, bubble stability, and wetting phenomena. Using the correct S.I. unit ensures formulas like rise in a capillary or pressure jump across a curved interface are applied consistently.
Given Data / Assumptions:
- Surface tension is force per unit length.
- Force in S.I. is newton (N).
- Length in S.I. is metre (m).
Concept / Approach:By definition, T = F / L. Therefore the unit must be N/m in S.I. This distinguishes surface tension from stress (N/m^2), density (kg/m^3), and dynamic viscosity (Pa·s). Remember this when decoding mixed-unit problem statements, especially those involving capillary tubes and contact angles.
Step-by-Step Solution:
State definition: T = F / L.Insert S.I. units: F → N; L → m; thus T → N/m.Confirm with typical values: water at room temperature ≈ 0.072 N/m.Verification / Alternative check:
Check capillary-rise formula where surface tension multiplies a length and cosine term, yielding force units, consistent with T in N/m.Why Other Options Are Wrong:
kg/m^3: density.kg/m^2 or kg/m: do not reduce to force/length.Pa·s: dynamic viscosity, not surface tension.Common Pitfalls:
Confusing surface tension with pressure (N/m^2) due to both involving forces.Expecting a mass-based unit because many fluid properties use kg and m^3; surface tension is fundamentally force/length.Final Answer:
N/m